In [1]:
import cupy as cp
import numpy as np
from time import perf_counter
from pyqcu import define
from pyqcu import io
from pyqcu import qcu
import cupyx.scipy.sparse.linalg as csla
from typing import Callable, Tuple, List
print('My rank is ', define.rank)
@@@@@@######QCU NOTES START######@@@@@@@
1. The libqcu.so was compiled when pyqcu setup in download_path/PyQCU/lib, please add this path to your LD_LIBRARY_PATH.
2. The QCU(PyQCU) splite grid by x->y->z->t, lattice by x->y->z->t->p->d->c->c or x->y->z->t->c->s(->p) and x->y->z->t->c->s->c->s(->p).
3. The QUDA(PyQUDA) splite grid by t->z->y->x, lattice by c->c->x->y->z->t->p->d or c->s->x->y->z->t(->p) and c->s->c->s->x->y->z->t(->p).
4. The QCU input params in numpy array(dtype=np.int32), argv in numpy array(dtype=np.float32 or float64) array, set_ptrs in numpy array(dtype=np.int64), other in cupy array(dtype=cp.complex64 or complex128).
5. The smallest lattice size is (x=4,y=4,z=4,t=8) that QCU support.
@@@@@@######QCU NOTES END######@@@@@@@
My rank is 0
In [ ]:
params = np.array([0]*define._PARAMS_SIZE_, dtype=np.int32)
params[define._LAT_X_] = 32
params[define._LAT_Y_] = 32
params[define._LAT_Z_] = 32
params[define._LAT_T_] = 32
params[define._LAT_XYZT_] = 1048576
params[define._GRID_X_] = 1
params[define._GRID_Y_] = 1
params[define._GRID_Z_] = 1
params[define._GRID_T_] = 1
params[define._PARITY_] = 0
params[define._NODE_RANK_] = 0
params[define._NODE_SIZE_] = 1
params[define._DAGGER_] = 0
params[define._MAX_ITER_] = 1e4
params[define._DATA_TYPE_] = 0
params[define._SET_INDEX_] = 2
params[define._SET_PLAN_] = 0
argv = np.array([0.0]*define._ARGV_SIZE_, dtype=np.float32)
argv[define._MASS_] = 0.0
argv[define._TOL_] = 1e-9
print("Parameters:", params)
print("Arguments:", argv)
Parameters: [ 32 32 32 32 1048576 1 1 1 1
0 0 1 0 10000 0 2 0]
Arguments: [0.e+00 1.e-09]
In [3]:
gauge_filename = f"quda_wilson-dslash-gauge_-{params[define._LAT_X_]}-{params[define._LAT_Y_]}-{params [define._LAT_Z_]}-{params[define._LAT_T_]}-{params[define._LAT_XYZT_]}-{params[define._GRID_X_]}-{params[define._GRID_Y_]}-{params[define._GRID_Z_]}-{params[define._GRID_T_]}-{params[define._PARITY_]}-{params[define._NODE_RANK_]}-{params[define._NODE_SIZE_]}-{params[define._DAGGER_]}-f.bin"
print("Gauge filename:", gauge_filename)
gauge = cp.fromfile(gauge_filename, dtype=cp.complex64,
count=params[define._LAT_XYZT_]*define._LAT_DCC_)
gauge = io.gauge2ccdptzyx(gauge, params)
print("Gauge:", gauge)
print("Gauge data:", gauge.data)
print("Gauge shape:", gauge.shape)
Gauge filename: quda_wilson-dslash-gauge_-32-32-32-32-1048576-1-1-1-1-0-0-1-0-f.bin
U: [ 0.9888613 +0.02130369j 0.07348315-0.02076806j -0.09857995+0.07842391j
-0.07511304-0.01086277j 0.9932049 -0.00666964j 0.04573338+0.07515373j
0.10230845+0.07397576j -0.03536638+0.08011071j 0.9880291 -0.01380186j]
_U: [ 0. +0.j 0. +0.j 0. +0.j
0. +0.j 0. +0.j 0. +0.j
0.10230846+0.07397576j -0.03536638+0.08011071j 0.9880291 -0.01380186j]
Gauge: 37748736
Gauge: [[[[[[[[ 9.88861322e-01+2.13036854e-02j
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...
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9.93692815e-01+2.71296632e-02j
9.83198285e-01-1.35139465e-01j]
[ 9.78720069e-01-1.98325142e-03j
9.93130803e-01-9.38011408e-02j
9.90836382e-01-1.12305813e-01j ...
9.83554542e-01-9.74838287e-02j
9.94794011e-01-2.02055369e-03j
9.74876165e-01+1.35392189e-01j]
[ 9.95233715e-01+2.84341853e-02j
9.97503757e-01-3.42967696e-02j
9.86279070e-01-4.83361930e-02j ...
9.97766435e-01+2.60710977e-02j
9.89815474e-01-4.06388864e-02j
9.84454930e-01-4.09127884e-02j]
...
[ 9.90951955e-01-5.80204092e-02j
9.91911471e-01-4.17012833e-02j
9.92456198e-01-1.14234556e-02j ...
9.89989579e-01+3.26828510e-02j
9.89661872e-01-1.81615970e-03j
9.75031555e-01+3.34803127e-02j]
[ 9.82086360e-01-8.24206248e-02j
9.96917069e-01+6.22219918e-03j
9.91833925e-01-5.89990094e-02j ...
9.95132446e-01-5.77796176e-02j
9.76508498e-01+5.26986681e-02j
9.69759405e-01+1.09316923e-01j]
[ 9.77466404e-01-1.75825626e-01j
9.86098170e-01+1.54656181e-02j
9.95830059e-01-2.89488360e-02j ...
9.69687998e-01-2.33844340e-01j
9.73142028e-01+8.84055793e-02j
9.76351976e-01-1.37854680e-01j]]
...
[[ 9.97041166e-01-2.33190898e-02j
9.81663465e-01+1.68743834e-01j
9.92810726e-01+7.69913569e-02j ...
9.91827130e-01-9.46760084e-03j
9.82575357e-01-1.01889715e-01j
9.91184592e-01-4.83878739e-02j]
[ 9.92326736e-01+9.60645154e-02j
9.91317511e-01-3.56840976e-02j
9.92937088e-01-4.93157916e-02j ...
9.94010031e-01+4.87456471e-02j
9.93812442e-01+1.65337194e-02j
9.84295368e-01-5.51280901e-02j]
[ 9.87445116e-01+8.13022535e-03j
9.91929889e-01+9.69947502e-02j
9.89831090e-01+1.71946976e-02j ...
9.92597640e-01+4.77729365e-02j
9.99109566e-01+1.62187666e-02j
9.94775236e-01+1.56874470e-02j]
...
[ 9.65493917e-01-1.50908813e-01j
9.69291031e-01+7.31750578e-02j
9.92072284e-01+2.26269523e-03j ...
9.92003024e-01+8.94998387e-02j
9.68693852e-01-1.35457143e-01j
9.92689788e-01+6.65792301e-02j]
[ 9.63562071e-01-1.34147942e-01j
9.87656713e-01-2.97176745e-03j
9.71306086e-01-5.56050241e-03j ...
9.70454276e-01+1.19548365e-01j
9.85312223e-01-8.92719626e-02j
9.76129591e-01+6.03280738e-02j]
[ 9.90023911e-01+5.19349687e-02j
9.96814549e-01+1.28967129e-02j
9.86090362e-01+5.48941270e-02j ...
9.87902701e-01-1.52926231e-02j
9.89921272e-01+4.95315380e-02j
9.85276461e-01-5.22483774e-02j]]
[[ 9.96478260e-01+3.82887162e-02j
9.94808912e-01-3.73382270e-02j
9.97911274e-01-2.74260510e-02j ...
9.84751225e-01-6.45348579e-02j
9.91316319e-01+2.30151787e-02j
9.71297026e-01+1.21417291e-01j]
[ 9.90487158e-01-9.97319967e-02j
9.97269154e-01+4.09824811e-02j
9.93274093e-01-6.83204755e-02j ...
9.74156499e-01+1.66722655e-01j
9.96088922e-01+6.14344552e-02j
9.75944340e-01+1.80472195e-01j]
[ 9.80137825e-01-3.25242057e-02j
9.96238589e-01-8.19443166e-03j
9.83536959e-01-4.05329764e-02j ...
9.72300410e-01+1.11450464e-01j
9.70654726e-01-1.63155526e-01j
9.92724180e-01+4.18733358e-02j]
...
[ 9.74617958e-01+1.67996828e-02j
9.82483387e-01+5.70351146e-02j
9.66885984e-01+1.75825179e-01j ...
9.87893879e-01+1.53177381e-02j
9.84604776e-01-5.83510334e-03j
9.87243831e-01+1.26613289e-01j]
[ 9.90917504e-01+3.77910696e-02j
9.87498939e-01-1.23531550e-01j
9.95261848e-01+5.42504042e-02j ...
9.85861957e-01-2.74544880e-02j
9.83909309e-01+1.07454151e-01j
9.95772123e-01-5.45856729e-03j]
[ 9.80439007e-01-1.21368796e-01j
9.92627084e-01-5.12746386e-02j
9.96057332e-01-5.91591336e-02j ...
9.98781979e-01-3.18981111e-02j
9.95732903e-01+6.23967759e-02j
9.90981519e-01+1.27822720e-03j]]
[[ 9.83889282e-01-5.33840954e-02j
9.93013024e-01-2.68412679e-02j
9.87258911e-01-1.45019397e-01j ...
9.75535095e-01+1.37851059e-01j
9.79064286e-01-3.43752354e-02j
9.87260044e-01-1.12760914e-02j]
[ 9.96899784e-01-5.62877133e-02j
9.83844161e-01-4.56487797e-02j
9.79288578e-01-5.00736665e-03j ...
9.87465262e-01+4.23426181e-02j
9.96232331e-01-2.79147569e-02j
9.93339241e-01+9.58476914e-04j]
[ 9.79844570e-01-4.22503706e-03j
9.80435312e-01-4.30875234e-02j
9.86860037e-01-1.23507664e-01j ...
9.82289970e-01+1.57409191e-01j
9.78417695e-01+1.98838543e-02j
9.69375253e-01-1.06659710e-01j]
...
[ 9.91334558e-01+5.89914247e-03j
9.89599168e-01+1.08037837e-01j
9.92483735e-01-2.71785613e-02j ...
9.83042955e-01+6.85607046e-02j
9.85138893e-01-1.03230432e-01j
9.94926035e-01+4.62608375e-02j]
[ 9.96221125e-01-4.49398458e-02j
9.94287491e-01+3.47633362e-02j
9.93404090e-01-8.02222863e-02j ...
9.69325900e-01-4.79393899e-02j
9.92115915e-01-5.35401218e-02j
9.92409110e-01+2.44176984e-02j]
[ 9.79039073e-01+1.51826754e-01j
9.86636817e-01-6.89331144e-02j
9.79794681e-01+8.45923647e-02j ...
9.84965742e-01-4.14918251e-02j
9.85355198e-01-4.42222990e-02j
9.93500471e-01-6.05962276e-02j]]]]]]]]
Gauge data: <MemoryPointer 0xb05600000 device=0 mem=<cupy.cuda.memory.PooledMemory object at 0x7fcc564bcd70>>
Gauge shape: (3, 3, 4, 2, 32, 32, 32, 16)
In [4]:
set_ptrs = np.array(params, dtype=np.int64)
print("Set pointers:", set_ptrs)
print("Set pointers data:", set_ptrs.data)
qcu.applyInitQcu(set_ptrs, params, argv)
Set pointers: [ 32 32 32 32 1048576 1 1 1 1
0 0 1 0 10000 0 2 0]
Set pointers data: <memory at 0x7fcc553b2980>
gridDim.x :4096
blockDim.x :128
host_params[_LAT_X_] :16
host_params[_LAT_Y_] :32
host_params[_LAT_Z_] :32
host_params[_LAT_T_] :32
host_params[_LAT_XYZT_] :524288
host_params[_GRID_X_] :1
host_params[_GRID_Y_] :1
host_params[_GRID_Z_] :1
host_params[_GRID_T_] :1
host_params[_PARITY_] :0
host_params[_NODE_RANK_]:0
host_params[_NODE_SIZE_]:1
host_params[_DAGGER_] :0
host_params[_MAX_ITER_] :10000
host_params[_SET_INDEX_]:2
host_params[_SET_PLAN_] :0
host_argv[_MASS_] :0.000000e+00
host_argv[_TOL_] :1.000000e-09
lat_2dim[_XY_] :512
lat_2dim[_XZ_] :512
lat_2dim[_XT_] :512
lat_2dim[_YZ_] :1024
lat_2dim[_YT_] :1024
lat_2dim[_ZT_] :1024
lat_3dim[_YZT_] :32768
lat_3dim[_XZT_] :16384
lat_3dim[_XYT_] :16384
lat_3dim[_XYZ_] :16384
lat_4dim :524288
grid_2dim[_XY_] :1
grid_2dim[_XZ_] :1
grid_2dim[_XT_] :1
grid_2dim[_YZ_] :1
grid_2dim[_YT_] :1
grid_2dim[_ZT_] :1
grid_3dim[_YZT_] :1
grid_3dim[_XZT_] :1
grid_3dim[_XYT_] :1
grid_3dim[_XYZ_] :1
grid_index_1dim[_X_] :0
grid_index_1dim[_Y_] :0
grid_index_1dim[_Z_] :0
grid_index_1dim[_T_] :0
move_wards[_B_X_] :0
move_wards[_B_Y_] :0
move_wards[_B_Z_] :0
move_wards[_B_T_] :0
move_wards[_F_X_] :0
move_wards[_F_Y_] :0
move_wards[_F_Z_] :0
move_wards[_F_T_] :0
move_wards[_BX_BY_] :0
move_wards[_BX_BZ_] :0
move_wards[_BX_BT_] :0
move_wards[_BY_BZ_] :0
move_wards[_BY_BT_] :0
move_wards[_BZ_BT_] :0
move_wards[_FX_BY_] :0
move_wards[_FX_BZ_] :0
move_wards[_FX_BT_] :0
move_wards[_FY_BZ_] :0
move_wards[_FY_BT_] :0
move_wards[_FZ_BT_] :0
move_wards[_BX_FY_] :0
move_wards[_BX_FZ_] :0
move_wards[_BX_FT_] :0
move_wards[_BY_FZ_] :0
move_wards[_BY_FT_] :0
move_wards[_BZ_FT_] :0
move_wards[_FX_FY_] :0
move_wards[_FX_FZ_] :0
move_wards[_FX_FT_] :0
move_wards[_FY_FZ_] :0
move_wards[_FY_FT_] :0
move_wards[_FZ_FT_] :0
set_ptr:0x55619355e2a0
long long set_ptr:93877572068000
lattice set init total time:0.048005424 sec
In [5]:
# give x, b, r, r_tilde, p, v, s, t
lat_t = params[define._LAT_T_]
lat_z = params[define._LAT_Z_]
lat_y = params[define._LAT_Y_]
lat_x = int(params[define._LAT_X_]/define._LAT_P_)
lat_d = define._LAT_D_
lat_s = define._LAT_S_
lat_p = define._LAT_P_
lat_c = define._LAT_C_
latt_shape = (lat_s, lat_c, lat_t, lat_z, lat_y, lat_x)
MAX_ITER = params[define._MAX_ITER_]
TOL = argv[define._TOL_]
N = params[define._LAT_XYZT_] * define._LAT_HALF_SC_
In [6]:
def _matvec(src, eigen_value=0.0):
print("norm src", cp.linalg.norm(src))
dest = cp.zeros(N, cp.complex64)
qcu.applyWilsonCgDslashQcu(dest, src, gauge, set_ptrs, params)
print("norm dest", cp.linalg.norm(dest))
return dest-src*eigen_value
In [7]:
# def power_iteration(matvec, v0, num_iter=params[define._MAX_ITER_], tol=argv[define._TOL_]):
# v = v0
# prev_v = cp.zeros_like(v)
# for i in range(num_iter):
# Av = matvec(v)
# v_new = Av / cp.linalg.norm(Av)
# diff = cp.linalg.norm(v_new - v)
# print(f"Iteration {i+1}: difference = {diff:.6e}")
# if diff < tol:
# print(
# f"Power Iteration converged after {i+1} iterations. Difference: {diff:.6e}")
# break
# v = v_new
# eigenvalue = cp.dot(v.conj().T, matvec(v))
# return eigenvalue, v
# def validate_power_iteration():
# v0 = cp.random.randn(N).astype(cp.complex64)
# eigenvalue, eigenvector = power_iteration(_matvec, v0)
# print("Dominant eigenvalue:", eigenvalue)
# print("Corresponding eigenvector:", eigenvector[:10])
# Ax = _matvec(eigenvector)
# eigenvalue_check = cp.dot(eigenvector.conj().T, Ax)
# print(f"Eigenvalue verification (v^T A v): {eigenvalue_check}")
# if cp.isclose(eigenvalue, eigenvalue_check):
# print("Validation passed: Eigenvalue calculation is correct.")
# else:
# print("Validation failed: Eigenvalue calculation is incorrect.")
# print("Eigenvector norm:", cp.linalg.norm(eigenvector))
# return eigenvalue, eigenvector
# eigenvalue, eigenvector = validate_power_iteration()
# print("Diff:", cp.linalg.norm(_matvec(eigenvector) -
# eigenvalue*eigenvector) / cp.linalg.norm(eigenvector))
In [8]:
# # bistabcg
# def dot(a, b):
# cp.cuda.runtime.deviceSynchronize()
# return cp.inner(a.flatten().conjugate(), b.flatten())
# def diff(a, b):
# cp.cuda.runtime.deviceSynchronize()
# return cp.linalg.norm(a - b) / cp.linalg.norm(b)
# def run(eigen_value):
# t0 = perf_counter()
# x = cp.random.rand(N).astype(cp.complex64)
# print("shape:", x.shape)
# b = cp.zeros(N, cp.complex64) # must be zero
# r = cp.zeros(N, cp.complex64)
# r_tilde = cp.zeros(N, cp.complex64)
# p = cp.zeros(N, cp.complex64)
# s = cp.zeros(N, cp.complex64)
# v = cp.zeros(N, cp.complex64)
# t = cp.zeros(N, cp.complex64)
# r = b - _matvec(x, eigen_value)
# r_tilde = r
# r_norm2 = 0
# rho_prev = 1
# rho = 0
# alpha = 1
# omega = 1
# beta = 0
# for i in range(MAX_ITER):
# # print("## rho:", rho)
# rho = dot(r_tilde, r)
# # print("## beta:", beta)
# beta = (rho / rho_prev) * (alpha / omega)
# p = r + (p - v * omega) * beta
# # v = A * p
# v = _matvec(p, eigen_value)
# # print("## alpha:", alpha)
# alpha = rho / dot(r_tilde, v)
# s = r - v * alpha
# # t = A * s
# t = _matvec(s, eigen_value)
# # print("## omega:", omega)
# omega = dot(t, s) / dot(t, t)
# x = x + p * alpha + s * omega
# r = s - t * omega
# r_norm2 = cp.linalg.norm(r)
# print("##{}# r_norm2:{}".format(i, r_norm2))
# _diff = diff(_matvec(x, 0.0), eigen_value*x)
# print("diff:", _diff)
# # break
# # if (r_norm2 < TOL or i == MAX_ITER - 1):
# # print("### turns:", i)
# # break
# if (_diff < TOL or i == MAX_ITER - 1):
# print("### turns:", i)
# break
# rho_prev = rho
# # print(" diff:", diff(_matvec(x, eigen_value), b))
# # print("x:", x)
# t1 = perf_counter()
# print("Time:", t1-t0)
# return x, _diff
# eigen_value = eigenvalue
# eigen_vector, _diff = run(eigen_value)
# print("eigen_vector:", eigen_vector)
# print("eigen_vector shape:", eigen_vector.shape)
# print("diff:", _diff)
In [9]:
# print("Difference:", cp.linalg.norm(eigenvector-eigen_vector)/cp.linalg.norm(eigenvector))
In [10]:
# import cupyx.scipy.sparse.linalg as csla
# define._LAT_E_ = 24
# A = csla.LinearOperator((N,
# N), matvec=_matvec, dtype=cp.complex64)
# evals, evecs = csla.eigsh(a=A, k=define._LAT_E_, which="SA",
# return_eigenvectors=True)
# print("evals:", evals)
# print("evecs:", evecs)
# cp.linalg.norm(_matvec(evecs[:, 0])-evals[0] *
# evecs[:, 0])/cp.linalg.norm(evals[0]*evecs[:, 0])
In [11]:
def shifted_power_iteration(
matvec,
n=N,
num_eigenvalues=define._LAT_E_,
max_iter=params[define._MAX_ITER_],
tol=argv[define._TOL_]
):
eigenvalues = []
eigenvectors = []
# 用于存储中间结果的缓冲区
v = cp.ndarray((n,), dtype=np.complex64)
w = cp.ndarray((n,), dtype=np.complex64)
# 存储累积位移
total_shift = 0.0
for k in range(num_eigenvalues):
# 随机初始化向量
v[:] = cp.random.rand(n) + 1j * cp.random.rand(n)
# 对已找到的本征向量进行正交化
for j in range(k):
projection = cp.dot(cp.conj(eigenvectors[j]), v)
v -= projection * eigenvectors[j]
# 归一化
v /= cp.linalg.norm(v)
# 幂迭代
eigenvalue = None
for iter_count in range(max_iter):
# 矩阵向量乘法
w = matvec(v)
# 应用位移
w += total_shift * v
# 计算瑞利商
new_eigenvalue = cp.dot(cp.conj(v), w)
# 归一化
norm = cp.linalg.norm(w)
if norm < tol: # 避免零向量
v[:] = cp.random.rand(n) + 1j * cp.random.rand(n)
continue
w /= norm
# 检查收敛性
if eigenvalue is not None:
_diff = abs(new_eigenvalue - eigenvalue)
print(f"第 {k} 个本征值的第 {iter_count} 次迭代: {_diff:.8f}")
if _diff < tol:
break
eigenvalue = new_eigenvalue
v[:] = w
# 存储结果并减去位移
if eigenvalue is not None:
eigenvalue -= total_shift
eigenvalues.append(eigenvalue)
eigenvectors.append(v.copy())
# 更新位移以找到下一个本征值
total_shift = eigenvalue.real
return eigenvalues, eigenvectors
eigenvalues, eigenvectors = shifted_power_iteration(_matvec)
# 验证结果
print("计算得到的本征值:")
for i, ev in enumerate(eigenvalues):
print(f"λ_{i} = {ev:.8f}")
# 验证本征向量
v = eigenvectors[i]
w = cp.zeros_like(v)
w = _matvec(v)
error = cp.linalg.norm(w - ev * v) / cp.linalg.norm(w)
print(f"相对误差: {error:.2e}")
norm src
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第 23 个本征值的第 1093 次迭代: 0.00000215 norm src 1.0000001 norm dest 1.5706116 第 23 个本征值的第 1094 次迭代: 0.00000238 norm src 1.0 norm dest 1.570614 第 23 个本征值的第 1095 次迭代: 0.00000215 norm src 0.99999994 norm dest 1.570616 第 23 个本征值的第 1096 次迭代: 0.00000143 norm src 1.0000001 norm dest 1.5706185 第 23 个本征值的第 1097 次迭代: 0.00000358 norm src 1.0 norm dest 1.5706207 第 23 个本征值的第 1098 次迭代: 0.00000167 norm src 1.0 norm dest 1.5706229 第 23 个本征值的第 1099 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706251 第 23 个本征值的第 1100 次迭代: 0.00000191 norm src 0.99999994 norm dest 1.5706271 第 23 个本征值的第 1101 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706295 第 23 个本征值的第 1102 次迭代: 0.00000286 norm src 1.0 norm dest 1.5706316 第 23 个本征值的第 1103 次迭代: 0.00000215 norm src 1.0000001 norm dest 1.5706338 第 23 个本征值的第 1104 次迭代: 0.00000238 norm src 1.0 norm dest 1.5706359 第 23 个本征值的第 1105 次迭代: 0.00000167 norm src 1.0 norm dest 1.5706382 第 23 个本征值的第 1106 次迭代: 0.00000238 norm src 1.0 norm dest 1.5706403 第 23 个本征值的第 1107 次迭代: 0.00000238 norm src 1.0 norm dest 1.5706425 第 23 个本征值的第 1108 次迭代: 0.00000167 norm src 1.0 norm dest 1.5706445 第 23 个本征值的第 1109 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706468 第 23 个本征值的第 1110 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706487 第 23 个本征值的第 1111 次迭代: 0.00000191 norm src 1.0 norm dest 1.5706509 第 23 个本征值的第 1112 次迭代: 0.00000262 norm src 1.0000001 norm dest 1.570653 第 23 个本征值的第 1113 次迭代: 0.00000215 norm src 1.0 norm dest 1.570655 第 23 个本征值的第 1114 次迭代: 0.00000167 norm src 1.0 norm dest 1.570657 第 23 个本征值的第 1115 次迭代: 0.00000191 norm src 0.99999994 norm dest 1.570659 第 23 个本征值的第 1116 次迭代: 0.00000191 norm src 0.99999994 norm dest 1.5706612 第 23 个本征值的第 1117 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706633 第 23 个本征值的第 1118 次迭代: 0.00000286 norm src 1.0 norm dest 1.5706652 第 23 个本征值的第 1119 次迭代: 0.00000119 norm src 0.99999994 norm dest 1.5706671 第 23 个本征值的第 1120 次迭代: 0.00000215 norm src 0.99999994 norm dest 1.5706692 第 23 个本征值的第 1121 次迭代: 0.00000167 norm src 0.99999994 norm dest 1.5706712 第 23 个本征值的第 1122 次迭代: 0.00000215 norm src 0.9999999 norm dest 1.5706731 第 23 个本征值的第 1123 次迭代: 0.00000191 norm src 1.0 norm dest 1.5706753 第 23 个本征值的第 1124 次迭代: 0.00000262 norm src 1.0 norm dest 1.5706773 第 23 个本征值的第 1125 次迭代: 0.00000191 norm src 1.0 norm dest 1.5706792 第 23 个本征值的第 1126 次迭代: 0.00000143 norm src 1.0 norm dest 1.5706812 第 23 个本征值的第 1127 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706831 第 23 个本征值的第 1128 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706849 第 23 个本征值的第 1129 次迭代: 0.00000167 norm src 1.0 norm dest 1.570687 第 23 个本征值的第 1130 次迭代: 0.00000238 norm src 1.0 norm dest 1.5706888 第 23 个本征值的第 1131 次迭代: 0.00000191 norm src 0.99999994 norm dest 1.5706906 第 23 个本征值的第 1132 次迭代: 0.00000143 norm src 1.0 norm dest 1.5706927 第 23 个本征值的第 1133 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706946 第 23 个本征值的第 1134 次迭代: 0.00000215 norm src 1.0 norm dest 1.5706965 第 23 个本征值的第 1135 次迭代: 0.00000167 norm src 1.0 norm dest 1.5706984 第 23 个本征值的第 1136 次迭代: 0.00000191 norm src 1.0 norm dest 1.5707002 第 23 个本征值的第 1137 次迭代: 0.00000191 norm src 1.0 norm dest 1.5707022 第 23 个本征值的第 1138 次迭代: 0.00000191 norm src 1.0 norm dest 1.570704 第 23 个本征值的第 1139 次迭代: 0.00000167 norm src 1.0 norm dest 1.5707057 第 23 个本征值的第 1140 次迭代: 0.00000215 norm src 0.99999994 norm dest 1.5707076 第 23 个本征值的第 1141 次迭代: 0.00000143 norm src 1.0 norm dest 1.5707093 第 23 个本征值的第 1142 次迭代: 0.00000238 norm src 0.99999994 norm dest 1.5707111 第 23 个本征值的第 1143 次迭代: 0.00000119 norm src 1.0 norm dest 1.5707129 第 23 个本征值的第 1144 次迭代: 0.00000215 norm src 1.0 norm dest 1.5707148 第 23 个本征值的第 1145 次迭代: 0.00000191 norm src 1.0 norm dest 1.5707166 第 23 个本征值的第 1146 次迭代: 0.00000191 norm src 0.9999999 norm dest 1.5707182 第 23 个本征值的第 1147 次迭代: 0.00000072 norm src 0.99999994 norm dest 1.57072 第 23 个本征值的第 1148 次迭代: 0.00000191 norm src 0.9999999 norm dest 1.5707217 第 23 个本征值的第 1149 次迭代: 0.00000191 norm src 1.0 norm dest 1.5707238 第 23 个本征值的第 1150 次迭代: 0.00000262 norm src 1.0000001 norm dest 1.5707254 第 23 个本征值的第 1151 次迭代: 0.00000167 norm src 1.0 norm dest 1.5707271 第 23 个本征值的第 1152 次迭代: 0.00000167 norm src 0.99999994 norm dest 1.5707287 第 23 个本征值的第 1153 次迭代: 0.00000119 norm src 1.0 norm dest 1.5707306 第 23 个本征值的第 1154 次迭代: 0.00000238 norm src 1.0 norm dest 1.5707322 第 23 个本征值的第 1155 次迭代: 0.00000119 norm src 1.0 norm dest 1.5707339 第 23 个本征值的第 1156 次迭代: 0.00000215 norm src 1.0 norm dest 1.5707357 第 23 个本征值的第 1157 次迭代: 0.00000143 norm src 1.0 norm dest 1.5707374 第 23 个本征值的第 1158 次迭代: 0.00000191 norm src 1.0 norm dest 1.570739 第 23 个本征值的第 1159 次迭代: 0.00000167 norm src 0.99999994 norm dest 1.5707406 第 23 个本征值的第 1160 次迭代: 0.00000048 norm src 1.0000001 norm dest 1.5707424 第 23 个本征值的第 1161 次迭代: 0.00000310 norm src 1.0 norm dest 1.570744 第 23 个本征值的第 1162 次迭代: 0.00000143 norm src 1.0 norm dest 1.5707457 第 23 个本征值的第 1163 次迭代: 0.00000215 norm src 1.0 norm dest 1.5707473 第 23 个本征值的第 1164 次迭代: 0.00000072 norm src 0.99999994 norm dest 1.5707488 第 23 个本征值的第 1165 次迭代: 0.00000143 norm src 0.99999994 norm dest 1.5707506 第 23 个本征值的第 1166 次迭代: 0.00000191 norm src 0.9999999 norm dest 1.570752 第 23 个本征值的第 1167 次迭代: 0.00000119 norm src 0.99999994 norm dest 1.5707537 第 23 个本征值的第 1168 次迭代: 0.00000167 norm src 0.99999994 norm dest 1.5707554 第 23 个本征值的第 1169 次迭代: 0.00000143 norm src 1.0 norm dest 1.570757 第 23 个本征值的第 1170 次迭代: 0.00000238 norm src 1.0 norm dest 1.5707585 第 23 个本征值的第 1171 次迭代: 0.00000167 norm src 1.0 norm dest 1.5707601 第 23 个本征值的第 1172 次迭代: 0.00000167 norm src 1.0000001 norm dest 1.5707617 第 23 个本征值的第 1173 次迭代: 0.00000143 norm src 1.0 norm dest 1.5707633 第 23 个本征值的第 1174 次迭代: 0.00000167 norm src 0.99999994 norm dest 1.5707648 第 23 个本征值的第 1175 次迭代: 0.00000119 norm src 1.0 norm dest 1.5707664 第 23 个本征值的第 1176 次迭代: 0.00000167 norm src 1.0 norm dest 1.5707679 第 23 个本征值的第 1177 次迭代: 0.00000167 norm src 1.0 norm dest 1.5707694 第 23 个本征值的第 1178 次迭代: 0.00000167 norm src 0.99999994 norm dest 1.5707709 第 23 个本征值的第 1179 次迭代: 0.00000095 norm src 0.99999994 norm dest 1.5707724 第 23 个本征值的第 1180 次迭代: 0.00000191 norm src 0.99999994 norm dest 1.570774 第 23 个本征值的第 1181 次迭代: 0.00000143 norm src 1.0 norm dest 1.5707755 第 23 个本征值的第 1182 次迭代: 0.00000191 norm src 0.9999999 norm dest 1.5707768 第 23 个本征值的第 1183 次迭代: 0.00000072 norm src 1.0 norm dest 1.5707785 第 23 个本征值的第 1184 次迭代: 0.00000191 norm src 1.0 norm dest 1.5707799 第 23 个本征值的第 1185 次迭代: 0.00000143 norm src 1.0 norm dest 1.5707814 第 23 个本征值的第 1186 次迭代: 0.00000167 norm src 1.0 norm dest 1.5707829 第 23 个本征值的第 1187 次迭代: 0.00000143 norm src 1.0 norm dest 1.5707843 第 23 个本征值的第 1188 次迭代: 0.00000143 norm src 0.9999999 norm dest 1.5707856 第 23 个本征值的第 1189 次迭代: 0.00000048 norm src 1.0000001 norm dest 1.5707873 第 23 个本征值的第 1190 次迭代: 0.00000286 norm src 0.99999994 norm dest 1.5707886 第 23 个本征值的第 1191 次迭代: 0.00000048 norm src 0.99999994 norm dest 1.57079 第 23 个本征值的第 1192 次迭代: 0.00000167 norm src 1.0 norm dest 1.5707915 第 23 个本征值的第 1193 次迭代: 0.00000167 norm src 1.0 norm dest 1.5707929 第 23 个本征值的第 1194 次迭代: 0.00000167 norm src 0.9999999 norm dest 1.5707942 第 23 个本征值的第 1195 次迭代: 0.00000048 norm src 1.0 norm dest 1.5707957 第 23 个本征值的第 1196 次迭代: 0.00000238 norm src 1.0 norm dest 1.5707971 第 23 个本征值的第 1197 次迭代: 0.00000095 norm src 1.0 norm dest 1.5707984 第 23 个本征值的第 1198 次迭代: 0.00000119 norm src 0.99999994 norm dest 1.5707998 第 23 个本征值的第 1199 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708013 第 23 个本征值的第 1200 次迭代: 0.00000238 norm src 0.9999999 norm dest 1.5708026 第 23 个本征值的第 1201 次迭代: 0.00000072 norm src 0.99999994 norm dest 1.570804 第 23 个本征值的第 1202 次迭代: 0.00000167 norm src 1.0 norm dest 1.5708054 第 23 个本征值的第 1203 次迭代: 0.00000143 norm src 1.0 norm dest 1.5708069 第 23 个本征值的第 1204 次迭代: 0.00000167 norm src 1.0 norm dest 1.5708082 第 23 个本征值的第 1205 次迭代: 0.00000143 norm src 1.0 norm dest 1.5708095 第 23 个本征值的第 1206 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708108 第 23 个本征值的第 1207 次迭代: 0.00000191 norm src 1.0 norm dest 1.5708121 第 23 个本征值的第 1208 次迭代: 0.00000119 norm src 0.9999999 norm dest 1.5708133 第 23 个本征值的第 1209 次迭代: 0.00000048 norm src 0.99999994 norm dest 1.5708146 第 23 个本征值的第 1210 次迭代: 0.00000119 norm src 0.99999994 norm dest 1.5708159 第 23 个本征值的第 1211 次迭代: 0.00000191 norm src 0.99999994 norm dest 1.5708172 第 23 个本征值的第 1212 次迭代: 0.00000119 norm src 1.0 norm dest 1.5708185 第 23 个本征值的第 1213 次迭代: 0.00000143 norm src 0.9999999 norm dest 1.5708197 第 23 个本征值的第 1214 次迭代: 0.00000072 norm src 0.9999999 norm dest 1.5708212 第 23 个本征值的第 1215 次迭代: 0.00000119 norm src 1.0 norm dest 1.5708224 第 23 个本征值的第 1216 次迭代: 0.00000167 norm src 1.0 norm dest 1.5708238 第 23 个本征值的第 1217 次迭代: 0.00000191 norm src 1.0 norm dest 1.5708249 第 23 个本征值的第 1218 次迭代: 0.00000095 norm src 0.9999999 norm dest 1.5708263 第 23 个本征值的第 1219 次迭代: 0.00000095 norm src 0.99999994 norm dest 1.5708274 第 23 个本征值的第 1220 次迭代: 0.00000119 norm src 1.0 norm dest 1.5708288 第 23 个本征值的第 1221 次迭代: 0.00000167 norm src 1.0 norm dest 1.57083 第 23 个本征值的第 1222 次迭代: 0.00000095 norm src 0.99999994 norm dest 1.5708312 第 23 个本征值的第 1223 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708325 第 23 个本征值的第 1224 次迭代: 0.00000143 norm src 1.0 norm dest 1.5708337 第 23 个本征值的第 1225 次迭代: 0.00000167 norm src 1.0 norm dest 1.5708349 第 23 个本征值的第 1226 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708362 第 23 个本征值的第 1227 次迭代: 0.00000143 norm src 0.99999994 norm dest 1.5708373 第 23 个本征值的第 1228 次迭代: 0.00000072 norm src 1.0 norm dest 1.5708386 第 23 个本征值的第 1229 次迭代: 0.00000143 norm src 1.0000001 norm dest 1.5708399 第 23 个本征值的第 1230 次迭代: 0.00000167 norm src 0.99999994 norm dest 1.5708407 第 23 个本征值的第 1231 次迭代: 0.00000048 norm src 1.0000001 norm dest 1.5708423 第 23 个本征值的第 1232 次迭代: 0.00000215 norm src 1.0 norm dest 1.5708435 第 23 个本征值的第 1233 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708444 第 23 个本征值的第 1234 次迭代: 0.00000119 norm src 1.0 norm dest 1.5708456 第 23 个本征值的第 1235 次迭代: 0.00000072 norm src 1.0000001 norm dest 1.5708468 第 23 个本征值的第 1236 次迭代: 0.00000167 norm src 1.0 norm dest 1.570848 第 23 个本征值的第 1237 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708492 第 23 个本征值的第 1238 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708501 第 23 个本征值的第 1239 次迭代: 0.00000119 norm src 0.99999994 norm dest 1.5708512 第 23 个本征值的第 1240 次迭代: 0.00000048 norm src 0.99999994 norm dest 1.5708524 第 23 个本征值的第 1241 次迭代: 0.00000143 norm src 1.0 norm dest 1.5708537 第 23 个本征值的第 1242 次迭代: 0.00000143 norm src 1.0 norm dest 1.5708548 第 23 个本征值的第 1243 次迭代: 0.00000095 norm src 1.0 norm dest 1.570856 第 23 个本征值的第 1244 次迭代: 0.00000167 norm src 1.0 norm dest 1.570857 第 23 个本征值的第 1245 次迭代: 0.00000072 norm src 0.99999994 norm dest 1.570858 第 23 个本征值的第 1246 次迭代: 0.00000072 norm src 1.0 norm dest 1.5708592 第 23 个本征值的第 1247 次迭代: 0.00000119 norm src 1.0 norm dest 1.5708601 第 23 个本征值的第 1248 次迭代: 0.00000143 norm src 0.99999994 norm dest 1.5708613 第 23 个本征值的第 1249 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708624 第 23 个本征值的第 1250 次迭代: 0.00000119 norm src 0.9999999 norm dest 1.5708634 第 23 个本征值的第 1251 次迭代: 0.00000048 norm src 1.0000001 norm dest 1.5708648 第 23 个本征值的第 1252 次迭代: 0.00000215 norm src 0.99999994 norm dest 1.5708656 第 23 个本征值的第 1253 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708667 第 23 个本征值的第 1254 次迭代: 0.00000072 norm src 1.0 norm dest 1.5708677 第 23 个本征值的第 1255 次迭代: 0.00000095 norm src 1.0 norm dest 1.5708688 第 23 个本征值的第 1256 次迭代: 0.00000167 norm src 0.9999999 norm dest 1.5708698 第 23 个本征值的第 1257 次迭代: 0.00000000 计算得到的本征值: λ_0 = 1.57109463+0.00000000j norm src 0.99999994 norm dest 1.5710948 相对误差: 3.58e-04 λ_1 = 1.57087529-0.00000000j norm src 0.99999994 norm dest 1.5708764 相对误差: 8.09e-04 λ_2 = 1.57083738-0.00000000j norm src 0.99999994 norm dest 1.570838 相对误差: 7.78e-04 λ_3 = 1.57078946-0.00000000j norm src 0.99999994 norm dest 1.5707906 相对误差: 9.31e-04 λ_4 = 1.57083857+0.00000000j norm src 1.0 norm dest 1.5708395 相对误差: 8.79e-04 λ_5 = 1.57089174-0.00000000j norm src 0.9999999 norm dest 1.5708926 相对误差: 7.77e-04 λ_6 = 1.57099640+0.00000000j norm src 0.9999999 norm dest 1.5709975 相对误差: 7.06e-04 λ_7 = 1.57102144+0.00000000j norm src 0.9999999 norm dest 1.5710222 相对误差: 6.51e-04 λ_8 = 1.57090056+0.00000000j norm src 1.0 norm dest 1.570901 相对误差: 7.21e-04 λ_9 = 1.57080543-0.00000000j norm src 0.9999999 norm dest 1.5708066 相对误差: 8.78e-04 λ_10 = 1.57096875+0.00000000j norm src 1.0 norm dest 1.5709695 相对误差: 7.75e-04 λ_11 = 1.57092178-0.00000000j norm src 1.0 norm dest 1.5709223 相对误差: 7.46e-04 λ_12 = 1.57087958+0.00000000j norm src 1.0 norm dest 1.5708804 相对误差: 7.56e-04 λ_13 = 1.57092583-0.00000000j norm src 0.99999994 norm dest 1.5709265 相对误差: 7.78e-04 λ_14 = 1.57090461-0.00000000j norm src 1.0 norm dest 1.5709051 相对误差: 7.55e-04 λ_15 = 1.57089937-0.00000000j norm src 0.99999994 norm dest 1.5709003 相对误差: 8.02e-04 λ_16 = 1.57094300+0.00000000j norm src 1.0 norm dest 1.5709435 相对误差: 6.91e-04 λ_17 = 1.57089722+0.00000000j norm src 0.99999994 norm dest 1.5708979 相对误差: 7.67e-04 λ_18 = 1.57095349+0.00000000j norm src 0.99999994 norm dest 1.5709542 相对误差: 6.83e-04 λ_19 = 1.57099140+0.00000000j norm src 0.9999999 norm dest 1.5709926 相对误差: 7.62e-04 λ_20 = 1.57095301-0.00000000j norm src 1.0 norm dest 1.5709535 相对误差: 7.53e-04 λ_21 = 1.57089889-0.00000000j norm src 0.99999994 norm dest 1.5709001 相对误差: 8.01e-04 λ_22 = 1.57089651-0.00000000j norm src 0.99999994 norm dest 1.5708969 相对误差: 7.64e-04 λ_23 = 1.57086885-0.00000000j norm src 0.9999999 norm dest 1.5708698 相对误差: 8.17e-04
In [12]:
eigenvalues
Out[12]:
[array(1.5710946+3.2514436e-11j, dtype=complex64), array(1.5708753-6.002665e-11j, dtype=complex64), array(1.5708374-3.1832315e-12j, dtype=complex64), array(1.5707895-3.9847237e-11j, dtype=complex64), array(1.5708386+7.298695e-11j, dtype=complex64), array(1.5708917-2.989964e-11j, dtype=complex64), array(1.5709964+1.1823431e-11j, dtype=complex64), array(1.5710214+5.684342e-12j, dtype=complex64), array(1.5709006+4.206413e-12j, dtype=complex64), array(1.5708054-4.9112714e-11j, dtype=complex64), array(1.5709687+6.0936145e-11j, dtype=complex64), array(1.5709218-4.5474735e-12j, dtype=complex64), array(1.5708796+9.094947e-13j, dtype=complex64), array(1.5709258-4.1097792e-11j, dtype=complex64), array(1.5709046-9.458745e-11j, dtype=complex64), array(1.5708994-2.2509994e-11j, dtype=complex64), array(1.570943+4.4110493e-11j, dtype=complex64), array(1.5708972+6.366463e-12j, dtype=complex64), array(1.5709535+3.6948222e-11j, dtype=complex64), array(1.5709914+5.2750693e-11j, dtype=complex64), array(1.570953-4.956746e-11j, dtype=complex64), array(1.5708989-2.3419489e-11j, dtype=complex64), array(1.5708965-5.9117156e-12j, dtype=complex64), array(1.5708688-6.366463e-12j, dtype=complex64)]
In [13]:
eigenvectors[0]
Out[13]:
array([ 0.00011019-3.3849868e-05j, -0.00019698-5.8493009e-05j,
0.00016907-2.1190083e-06j, ..., 0.00023352+1.0564764e-04j,
-0.00028323-1.2248049e-04j, 0.00031611+6.1884180e-05j],
dtype=complex64)
In [14]:
eigenvectors[1]
Out[14]:
array([-0.00016843-4.3366521e-04j, 0.0002561 +3.4370035e-04j,
-0.00010726-4.1487903e-04j, ..., 0.00034043-9.5846306e-05j,
-0.00050256+1.2186132e-04j, 0.00043388-8.7990644e-05j],
dtype=complex64)
In [15]:
eigenvectors[2]
Out[15]:
array([-0.00030464+7.2071234e-05j, 0.00022192+1.3316350e-04j,
-0.00023817-1.4252070e-04j, ..., -0.00026966-1.7527273e-04j,
0.00020242+1.3561420e-04j, -0.00021154-1.2906564e-04j],
dtype=complex64)
In [16]:
eigenvectors[3]
Out[16]:
array([-0.00024654+2.6417947e-05j, 0.00020589-1.2865798e-04j,
-0.00028624+1.0180634e-04j, ..., 0.00030569-2.8551219e-04j,
-0.00010088+1.4407843e-04j, 0.00020402-2.9525341e-04j],
dtype=complex64)
In [17]:
eigenvectors[8]
Out[17]:
array([-2.1568088e-04-3.7905786e-05j, 1.1930928e-04+5.8005251e-05j,
-1.0789587e-04-6.9251844e-05j, ..., 1.4028237e-04-3.2521324e-04j,
4.8712227e-05+2.4246574e-04j, -2.9026256e-05-2.1543294e-04j],
dtype=complex64)
In [18]:
eigenvectors[7]
Out[18]:
array([ 0.00032246+1.8667255e-04j, -0.00022841-1.3719682e-04j,
0.00023254+2.4205162e-04j, ..., 0.00012554+5.5392633e-05j,
-0.0002477 +1.3193564e-04j, 0.00033989-1.4686681e-04j],
dtype=complex64)
In [19]:
eigen_index = 8
print("Diff:", cp.linalg.norm(_matvec(eigenvectors[eigen_index]) -
eigenvalues[eigen_index]*eigenvectors[eigen_index]) / cp.linalg.norm(eigenvectors[eigen_index]))
norm src 1.0 norm dest 1.570901 Diff: 0.0011322624
In [20]:
for i, ev in enumerate(eigenvalues):
print(f"λ_{i} = {ev:.8f}")
# 验证本征向量
v = eigenvectors[i]*1e6
print(f"v_{i} = {v}")
w = cp.zeros_like(v)
w = _matvec(v)
error = cp.linalg.norm(w - ev * v) / cp.linalg.norm(w)
print(f"相对误差: {error:.2e}")
j = i+1
if i == len(eigenvalues)-1:
j = 0
eigen_diff = cp.linalg.norm(
eigenvectors[i]-eigenvectors[j])/cp.linalg.norm(eigenvectors[i])
print(f"本征向量{i}与本征向量{j}的相对误差:{eigen_diff:.2e}")
λ_0 = 1.57109463+0.00000000j
v_0 = [ 110.19172 -33.84987j -196.97662 -58.493008j 169.0651 -2.1190083j
... 233.5238 +105.64764j -283.23187-122.480484j
316.10928 +61.884182j ]
norm src 1000000.0
norm dest 1571094.6
相对误差: 3.58e-04
本征向量0与本征向量1的相对误差:1.42e+00
λ_1 = 1.57087529-0.00000000j
v_1 = [-168.42702 -433.6652j 256.1002 +343.70035j -107.259636-414.87903j
... 340.42728 -95.846306j -502.56116 +121.86132j
433.88382 -87.99065j ]
norm src 999999.94
norm dest 1570876.4
相对误差: 8.09e-04
本征向量1与本征向量2的相对误差:1.43e+00
λ_2 = 1.57083738-0.00000000j
v_2 = [-304.6362 +72.071236j 221.92036+133.1635j -238.16966-142.5207j ...
-269.6599 -175.27272j 202.41771+135.6142j -211.53885-129.06564j ]
norm src 999999.94
norm dest 1570838.0
相对误差: 7.78e-04
本征向量2与本征向量3的相对误差:1.41e+00
λ_3 = 1.57078946-0.00000000j
v_3 = [-246.5437 +26.417948j 205.8921 -128.65797j -286.23804+101.80634j ...
305.6901 -285.51218j -100.88299+144.07843j 204.02196-295.25342j ]
norm src 999999.94
norm dest 1570790.5
相对误差: 9.31e-04
本征向量3与本征向量4的相对误差:1.41e+00
λ_4 = 1.57083857+0.00000000j
v_4 = [ -40.820797 +30.650171j 121.91324 -85.02151j -238.41843 +152.1113j
... 38.04143 -553.64685j 266.6846 +591.98065j
-132.45296 -678.05225j ]
norm src 999999.94
norm dest 1570839.6
相对误差: 8.79e-04
本征向量4与本征向量5的相对误差:1.41e+00
λ_5 = 1.57089174-0.00000000j
v_5 = [ -58.202316 +599.9151j 1.9449369-651.8865j -20.99789 +617.88306j
... -141.45654 +489.07758j -8.781775 -394.24646j
19.491774 +347.37027j]
norm src 999999.94
norm dest 1570892.5
相对误差: 7.77e-04
本征向量5与本征向量6的相对误差:1.41e+00
λ_6 = 1.57099640+0.00000000j
v_6 = [ 463.5643 -238.84076j -446.01474+287.80875j 421.00568-253.52501j ...
-487.91336 +35.79339j 260.85455-114.044136j -415.89636+101.2075j ]
norm src 999999.94
norm dest 1570997.5
相对误差: 7.06e-04
本征向量6与本征向量7的相对误差:1.41e+00
λ_7 = 1.57102144+0.00000000j
v_7 = [ 322.45557+186.67255j -228.40799-137.19682j 232.54373+242.05162j ...
125.53771 +55.39263j -247.69728+131.93564j 339.8872 -146.8668j ]
norm src 999999.94
norm dest 1571022.1
相对误差: 6.51e-04
本征向量7与本征向量8的相对误差:1.42e+00
λ_8 = 1.57090056+0.00000000j
v_8 = [-215.68088 -37.905785j 119.30928 +58.005253j -107.89587 -69.25185j
... 140.28236 -325.21326j 48.712227+242.46574j
-29.026257-215.43294j ]
norm src 1000000.0
norm dest 1570901.1
相对误差: 7.21e-04
本征向量8与本征向量9的相对误差:1.43e+00
λ_9 = 1.57080543-0.00000000j
v_9 = [ 344.97617 -38.126987j -250.47763 +47.23441j 169.48782 -50.32828j ...
144.94064-227.73448j -244.6966 +297.63138j 196.98985-358.6684j ]
norm src 999999.94
norm dest 1570806.8
相对误差: 8.78e-04
本征向量9与本征向量10的相对误差:1.43e+00
λ_10 = 1.57096875+0.00000000j
v_10 = [-129.90897-381.7529j 93.37714+501.07394j -65.39111-599.5287j ...
655.6552 -21.895672j -683.28925 +12.878436j 680.4141 -72.449005j]
norm src 999999.94
norm dest 1570969.5
相对误差: 7.75e-04
本征向量10与本征向量11的相对误差:1.41e+00
λ_11 = 1.57092178-0.00000000j
v_11 = [-121.22787+695.9635j 182.67911-690.58325j -280.29626+706.19086j ...
239.62527+104.38387j -414.80487-236.8881j 361.34283+228.88937j]
norm src 1000000.0
norm dest 1570922.2
相对误差: 7.46e-04
本征向量11与本征向量12的相对误差:1.43e+00
λ_12 = 1.57087958+0.00000000j
v_12 = [ -21.943739 -86.00619j 80.26179 +170.22855j
1.3971834 +52.054836j ... -385.77673 +94.064285j
622.78265 -113.18395j -568.748 +45.43582j ]
norm src 999999.94
norm dest 1570880.4
相对误差: 7.56e-04
本征向量12与本征向量13的相对误差:1.41e+00
λ_13 = 1.57092583-0.00000000j
v_13 = [ 158.2305 +145.47247j -104.19043 -227.36905j 245.36418 +164.66583j ...
-69.85509 +263.15683j 120.93825 -147.52397j -103.269615+101.64767j]
norm src 999999.94
norm dest 1570926.5
相对误差: 7.78e-04
本征向量13与本征向量14的相对误差:1.42e+00
λ_14 = 1.57090461-0.00000000j
v_14 = [ 84.78046 +85.95987j -37.41109 -142.95149j 62.354725+295.85226j ...
82.32612 -173.09746j -51.33811 +183.3928j 97.629425 -93.42162j]
norm src 1000000.06
norm dest 1570905.1
相对误差: 7.55e-04
本征向量14与本征向量15的相对误差:1.42e+00
λ_15 = 1.57089937-0.00000000j
v_15 = [ -9.087385+134.74391j -99.95212 -239.5371j 15.379323 +32.093258j
... -773.3928 +119.23577j 738.3085 -196.06712j
-630.05444 +360.8405j ]
norm src 999999.94
norm dest 1570900.4
相对误差: 8.02e-04
本征向量15与本征向量16的相对误差:1.43e+00
λ_16 = 1.57094300+0.00000000j
v_16 = [-176.36221 -257.47107j 237.45447 +382.26614j -163.36661 -386.5899j
... -92.916664 +91.919014j 286.11893 -156.5727j
-158.18794 -43.95432j ]
norm src 1000000.0
norm dest 1570943.5
相对误差: 6.91e-04
本征向量16与本征向量17的相对误差:1.41e+00
λ_17 = 1.57089722+0.00000000j
v_17 = [-167.49866 +277.6496j 41.2842 -143.78377j -57.657604+248.60416j ...
-132.83894 +288.1332j 263.88452 -229.12154j -322.7842 +215.67627j]
norm src 1000000.0
norm dest 1570898.0
相对误差: 7.67e-04
本征向量17与本征向量18的相对误差:1.42e+00
λ_18 = 1.57095349+0.00000000j
v_18 = [ 386.8991 +584.85675j -286.46277-569.4879j 296.56204+486.68268j ...
-298.36572-248.60835j 361.97626+124.00337j -393.24637-276.65213j]
norm src 999999.94
norm dest 1570954.1
相对误差: 6.83e-04
本征向量18与本征向量19的相对误差:1.42e+00
λ_19 = 1.57099140+0.00000000j
v_19 = [-414.9875 -677.5721j 324.04956+589.9055j -361.40582-604.278j ...
-268.78024 -18.964245j 198.30484+171.33107j -176.90143-139.13943j ]
norm src 999999.9
norm dest 1570992.5
相对误差: 7.62e-04
本征向量19与本征向量20的相对误差:1.40e+00
λ_20 = 1.57095301-0.00000000j
v_20 = [ 131.3372 -377.5479j -234.77895+379.71188j 338.15387-492.8778j ...
-389.25693-346.42773j 369.41122+184.14081j -561.11755-103.37218j]
norm src 999999.94
norm dest 1570953.6
相对误差: 7.53e-04
本征向量20与本征向量21的相对误差:1.44e+00
λ_21 = 1.57089889-0.00000000j
v_21 = [ 203.76662 +444.30246j -105.61026 -412.67868j 233.31195 +246.279j ...
-61.440247+353.02307j 245.15659 -395.8376j -100.93443 +208.14188j]
norm src 999999.94
norm dest 1570900.0
相对误差: 8.01e-04
本征向量21与本征向量22的相对误差:1.43e+00
λ_22 = 1.57089651-0.00000000j
v_22 = [-537.91595-416.83356j 608.7422 +359.76038j -638.08795-454.4591j ...
283.41653+203.56702j -446.0495 -64.08735j 423.47617 +74.40231j]
norm src 999999.94
norm dest 1570896.9
相对误差: 7.64e-04
本征向量22与本征向量23的相对误差:1.43e+00
λ_23 = 1.57086885-0.00000000j
v_23 = [ 150.28822 -5.798119j -228.17564 -36.502472j 187.62167+165.91678j ...
287.64566+280.93304j -257.25824-301.7333j 370.39883+179.29327j ]
norm src 999999.9
norm dest 1570869.8
相对误差: 8.17e-04
本征向量23与本征向量0的相对误差:1.42e+00
In [21]:
# qcu.applyEndQcu(set_ptrs, params)